Washington — First came the challenges of getting people enrolled. Now another hurdle for the Affordable Care Act is coming into focus: ensuring that Americans actually get the health insurance they’re paying for.

Many people who signed up for insurance using an Obamacare exchange did so months ago and are already relying on their new health plans to help with medical bills.

By some accounts, the implementation of Obamacare is moving forward without widespread problems – even though the administrative “back end” of the federal website HealthCare.gov is still a work in progress. But that doesn’t mean it is going seamlessly. Challenges include:

Difficulty getting insurers to acknowledge that individuals have enrolled. Nevada is an early case in point. The state created its own enrollment website under the law, and now faces a class-action lawsuit by consumers who say they aren’t getting the insurance they paid for.

Consumer setbacks involving “narrow networks.” Some enrollees are frustrated – or say their health is put at risk – by not having as much choice of doctors and or specialized care centers within their plan as they had hoped.

Payment-processing glitches. Some Americans have faced temporary lapses in coverage when their payments haven’t flowed smoothly through an Obamacare exchange to their insurance firm. Intervention by elected officials helped to resolve one recent case.

All this suggests that the implementation of Obamacare is hardly glitch-free. But while words like “disaster” and “debacle” dogged the website launch in October, the problems lately appear to be relatively isolated.

“The error rate [in connecting applicants with insurers] has gone down substantially,” compared with the website’s early weeks last fall, says Sabrina Corlette, a senior research fellow at Georgetown University’s Center on Health Insurance Reforms.

“We’re not hearing of major problems” or customer complaints, she says, citing anecdotal evidence from state-based “navigators,” who help support Obamacare enrollees.

But it’s still early. Many enrollees entered the system in late March and won’t see coverage start until May, says Larry Levitt, a health reform expert at the Kaiser Family Foundation. And since most people don’t immediately rush to arrange a doctor or hospital visit right after getting covered, evidence of other problems could emerge later this spring and beyond, he adds.

So far, some of the biggest challenges have arisen in states that created their own websites for insurance shopping.

Getting what enrollees paid for

In Nevada, the recently filed lawsuit alleges that numerous state residents have been going uncovered despite enrolling and paying for insurance.

The lawsuit says that one plaintiff, Larry Basich, had a heart attack at the end of last year and required costly surgery on Jan. 3 – in theory the third day of his new insurance. But the legal complaint says his payment wasn’t processed properly, leaving Mr. Basich stuck with more than $400,000 in bills.

“Our lawsuit isn’t against Obamacare, [it’s] about the state of Nevada's implementation of it,” says attorney Mitchell Bisson, with the firm Callister Immerman & Associates.

Mr. Bisson says plaintiffs have been adding their names steadily – about 80 so far and many more expected – since the firm filed its initial complaint on April 1. As he sees it, the problems in Nevada were much more severe than in the rest of the country.

The lawsuit alleges that due to failures by the state and its website contractor, Xerox State Health Care, as many as 10,000 applicants may have paid “yet either do not have health insurance coverage to date, or received a coverage effective date different than that for which they paid.”

In some other states, individuals say they’ve been through similar challenges. Washington State resident Jessica Farber says she paid for an Obamacare policy to start in March, when she moved to Seattle from South Carolina.

As Ms. Farber was trying to complete her enrollment on the state’s website in February, she says a glitch occurred that resulted in countless hours on the phone and mixed signals about her status: First the state said her enrollment would have to be cancelled and that she would get a refund, and later the state said it had provided her with insurance for the month of March (so she will get no refund).

“I was able to continue my insurance from the state I was in before, thank God,” says Farber, who says she requires costly prescription drugs for a chronic illness.

Farber’s coverage with Premera Blue Cross in Washington is now up and running. But for March, she ended up paying in two states, and has resigned herself to feeling lucky to have had coverage that month at all.

In fact, for Farber a larger lesson is a positive one: Thanks to the health reform law she can now sign up for insurance on her own in any state, despite her preexisting condition. She doesn't have to worry about whether her husband will have an employer-sponsored health plan that covers them both. (She says he once lost a job because of her medical costs.)

What are 'narrow networks'?

Around the country, other challenges have also been surfacing.

Many enrollees have voiced concern about what’s known as “narrow networks,” in which insurers have held down costs by providing access only to selected hospitals and physician groups. Enrollees need to do their homework in they want to find a plan that offers access to a particular hospital or to specialized care facilities such as a cancer treatment center.

“There is a lot of dissatisfaction being communicated from consumers to insurance company call centers and their agents about the new health insurance plans, particularly compared to the plans people are used to,” insurance industry consultant Robert Laszewski wrote recently.

The plight of Margaret Figueroa in New York State garnered news headlines this month as the Staten Island resident told of losing access to specialized doctors and treatments for her chronic condition. For now, her former doctor has offered pro bono care while she seeks a longer-term answer. The physician said “there are a lot of patients falling through the cracks,” according to a news article on the Staten Island Advance website.

Payment glitches

In some cases, glitches in coverage have emerged even after people have been enrolled for a while.

In Washington State, Scott Fontenot started using his Obamacare plan in January and says he relies on it for prescriptions related to his experience of strokes, brain surgery, and lingering after-effects. But in March, he says his payment “didn't go from the exchange to my insurer for 14 to 15 days,” exhausting a grace period for payment.

Mr. Fontenot paid for some of his drugs a la carte this month before his coverage kicked back into place, and he says he’ll now be trying to send payments a couple of weeks earlier to avoid the risk of that happening again.

Along with the instances of customer tribulation, voices of gratitude have also emerged.

Pennsylvania resident Jeanne Goe, after having a diagnosis and starting treatment under her new insurance, sent a note to President Obama, saying, “I will be fighting just as you have been fighting for my life as a working American citizen.”